关于一些二进制数列的族复杂度和互相关测度  

On the f-complexity and cross-correlation of some binary sequences

作　　者：梁嘉怡 王晓瑛 Liang Jiayi;Wang Xiaoying(School of Mathematics,Northwest University,Xi′an 710127,China)

机构地区：[1]西北大学数学学院,陕西西安710127

出　　处：《纯粹数学与应用数学》2021年第3期318-326,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(11571277);陕西省工业科技攻关项目(2016GY-077).

摘　　要：构造具有大的f-复杂度和小的互相关测度的伪随机二进制数列族,是信息安全领域中非常困难的问题.本文利用Legendre符号与多项式特征和的估计,构造了两类具有较大的f-复杂度和较小的互相关测度的二进制数列族.It is very difficult to construct large family of pseudorandom binary sequences with large f-complexity and small cross-correlation measure.In this paper we give two large families of binary sequences and show that they enjoy large f-complexity and small cross-correlation measure by using the Legendre symbol and estimates for character sums of polynomials.

关 键 词：二进制数列 f-复杂度 互相关测度 多项式特征和 

分 类 号：O156.4[理学—数学]